Predicting Structure in Sparse Matrix Computations
SIAM Journal on Matrix Analysis and Applications
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Parallel scalability study of hybrid preconditioners in three dimensions
Parallel Computing
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A hybrid linear solver based on the Schur complement method has great potential to be a general purpose solver scalable on tens of thousands of processors. For this, it is imperative to exploit two levels of parallelism; namely, solving independent subdomains in parallel and using multiple processors per subdomain. This hierarchical parallelism can lead to a scalable implementation which maintains numerical stability at the same time. In this framework, load imbalance and excessive communication, which can lead to performance bottlenecks, occur at two levels: in an intra-processor group assigned to the same subdomain and among inter-processor groups assigned to different subdomains. We developed several techniques to address these issues, such as taking advantage of the sparsity of right-hand-sides during the triangular solutions with interfaces, load balancing sparse matrix-matrix multiplication to form update matrices, and designing an effective asynchronous point-to-point communication of the update matrices. We present numerical results to demonstrate that with the help of these techniques, our hybrid solver can efficiently solve large-scale highly-indefinite linear systems on thousands of processors.